This study investigated whether task complexity may affect L2 speaking performance as predicted by the Cognition Hypothesis (Robinson, 2011), and whether the effect of task complexity may interact with individual differences in working memory capacity. A total of twenty Korean advanced-level EFL learners performed two separate picture description tasks, which were different in task complexity along [+/- here and now] dimension. Their working memory was measured by an L1 version of a reading span task. The results showed that there was no significant difference between Here-and-Now task (i.e., a simple task) and There-and-Then task (i.e., a complex task) in terms of complexity, accuracy, and fluency of English speaking performance, rejecting the prediction of the Cognition Hypothesis. Yet, it found that working memory correlated with accuracy in L2 performance on the complex task, but not on the simple task. This indicates that the effect of individual learners' working memory capacity is observable only when a task demands a high control of attentional resources. Conversely, when a task is simple, individual differences in working memory capacity do not result in significant differences in L2 speaking performance.